Within the original structure (four one-poles in series with feedback
around them), try various transforms from to :

Backward difference:

Bilinear:

Problem:Delay-free loops: These transforms cause
the one-poles to have delay-free paths. Adding a delay to the
loop changes the structure, so that complete orthogonality is no
longer true (before the added delay, the bilinear case wasorthogonal).

Separation tables become necessary: The table we will use,
in the bilinear-transform case,
is a one-dimensional table that contains the feedback gain
necessary to make the filter unstable, indexed by .
We scale by this table (
).

We would like to find a structure for which a separation
table is unnecessary.